Synchronization of two non-identical coupled exciters in a non-resonant vibrating system of plane motion

In the average method of modified small parameters, the synchronization of two coupled exciters is converted to a problem on the existence and stability of zero solutions for the average differential equations of small parameters over the average period of two exciters. To implement frequency capture, the torque of frequency capture should be greater than or equal to the absolute value of the difference between the residual electromagnetic torques of the two motors. Because each exciter is involved in the motion of the vibrating system it has excited, its relative moment of inertia is reduced. The reduction is proportional to half its coefficient of cosine effect of phase angles (CCEPA). Because one of the exciters is involved in the motion excited by the other, a coupled moment of inertia exists for the two exciters. The stability of the synchronization of the two exciters is affected by the reduction of their relative moments of inertia and their moment of coupling inertia. For the synchronization to be stable, two conditions must be satisfied: (1) the non-dimensional relative moments of inertia of the two exciters are all greater than zero, and (2) four times the product of their non-dimensional relative moments is greater than the square of the coefficient of coupled cosine effect (CCCPA). The stability of synchronization depends solely on the ratios of the masses of the two exciters to the mass of the vibrating system and the ratio of the distance between one exciter and the centroid of the rigid frame to the equivalent rotating radius of the vibrating system about its centroid of the rigid frame, and is independent of the parameters of the two induction motors.